Pie with square

[Pekis]

Well, for curious people, here is the solution:

1) I will consider that the circle has a radius equal to 1, in order to express the d and e values directly in % of the radius of a circle of any size
2) The surface of the circle is then PI*1^2=PI, which implies that each part must have a surface equal to PI/9
3) All the parts with the same color have the same form
4) I will work with e'=e/2 and d'=d/2 to simplify calculations

Surface of the orange square:
e'^2*4, which must be equal to PI/9
=> e'=SQRT(PI)/6=0.295409 approx.
=> e=2*e'=SQRT(PI)/3
e=0.590818 approx.

Surface of the top yellow strip:
2*(integ(SQRT(1-x^2),x,0,d')-d'*e'), which must be equal to PI/9

(with integ(SQRT(1-x^2),x,0,d') to integrate the right part, -d'*e' to discard it's orange part, and *2 to add the left part)

=> d'=0.251508 approx. (using a solver)
=> d=2*d'
d=0.503016 approx.

Since 5 parts (4 yellow and 1 orange) of the surface of the pie are now known as 5*(PI/9), the 4 remaining red parts which have the same form share 4*(PI/9) => each has it's surface equal to PI/9:

Check Surface of the left top red part:
integ(SQRT(1-x^2),x,d',1)-(PI/9)/2-e'*(e'-d'), which is naturally equal to PI/9 !

(with integ(SQRT(1-x^2),x,d',1) to integrate starting from the right, -(PI/9)/2 to discard the half of the left yellow strip, and -e'*(e'-d') to discard it's small orange part)

Thanks for reading